Small arms no. Ammunition supply issues alone meant there was little point in distributing such weapons, and Germany was able to produce enough small arms. In any case, the main 'teeth' of a German platoon was its complement of MG42 machine guns, with much of the rest of the infantry acting as ammunition carriers (to generalise somewhat). This applies only to France 1944: early in the war the Germans were using all sorts of captured weapons as Germany's re-armament was too big a job, and units invading France and Russia had all sorts of captured equipment from rifles to tanks. Over time, this was replaced, lost or relegated to training and other 'second line' duties.

But the use of captured artillery and vehicles was extremely common. Many of the fortifications of the Westwall (French coastal defences) were emplaced with guns taken from the Czechs, French or Poles. This was simply prudent: as emplaced weapons they did not need to be mobile and it could be assumed they'd only ever fight with what was at hand, successfully or otherwise. The Germans had taken over many fortifications from the Czech Sudetenland and the Maginot Line, so re-deploying their guns made perfect sense. The Germans designed standardised bunkers that could accept various obsolete tank turrets as main armament. Even the steel 'hedgehogs' were often taken from captured forts.

Western Allied tanks were still vulnerable to AP shot from weapons such as the French 75mm or even Czech 47mm, weapons like the PaK-40 being in short supply and given to the Panzer and Panzergrenadier divisons that made up the teeth of the defences.

Germany captured huge numbers of Soviet guns in 1941, notably their 76mm field/AT gun, and this was a standard issue of sorts for some time afterward, and was encountered in North Africa. However, its use in France seems minimal. Most would have been used in Russia both for obvious reasons of transport and ammo supply (many were modified to take German ammunition according to Ian Hogg), and because the Wehrmacht in 1942 and 43 needed anything that could knock out a T-34.

In the desperation to increase Germany's mobile armoured force in France in the months before summer 1944 (the obvious period when invasion was likely), many units were padded out with captured weapons. The 21st Panzer Division had a company of obsolete German tanks taken from training schools, a company of French tanks, and an attached tank destroyer battalion based on improvised/modified French vehicles (chassis fitted with modern German guns). Another recently-raised SS division attacked US paratroopers outside Carentan with 1940-vintage Hotchkiss tanks.

By July 1944 many of these weapons were destroyed or captured, and the German army in Normandy fought its last battles with more recognisably-Wehrmacht equipment.

But the defeat in August 1944 saw German units losing most of their equipment, and being re-equipped in the Netherlands and on the German border. Operation Market-Garden was famously opposed by the 9th and 10th SS Panzer Divisions, re-equipping after being ground down around Vire in Normandy. Its reconnaissance unit, largely destroyed in a charge on Arnhem Bridge, was equipped with a hodge-podge of scraped up equipment so diverse that it's exact constitution remains a mystery. XXX Corps was opposed by French 75mm guns (the Germans gave them new carriages and a muzzle brake) used in the anti-tank role, while early marks of Panzer MkIII were destroyed outside Nijmegen. These had all been requisitioned in haste from police units, training schools and coastal defence units.